This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p...This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.展开更多
This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asympto...This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the linear version of the above ODE, by taking and study its Lyapunov stability. Exploiting the similarities between linear and nonlinear ODE, we construct a Lyapunov function for the stability analysis of the given nonlinear differential equation.展开更多
基金Supported by the Natural Seience Foundation of Henan Educational Committee(20031100036)
文摘This paper discussed asymptotic property of Taylor remainder 'mean value point' in normed Linear space. The asymptotic progerty of 'mean value point' is solved when f(n+i)(x0)h(n+i) = 0(i = 1, 2,..., p - 1) and f(n+p)(x0)h(h+p) don't exist. Meanwhile, achieve more general asymptotic estimation formula. Make many former results are just because of special case of the pager.
文摘This paper is concerned with the stability analysis of nonlinear third order ordinary differential equations of the form . We construct a suitable Lyapunov function for this purpose and show that it guarantees asymptotic stability. Our approach is to first consider the linear version of the above ODE, by taking and study its Lyapunov stability. Exploiting the similarities between linear and nonlinear ODE, we construct a Lyapunov function for the stability analysis of the given nonlinear differential equation.
